Computer Science – Information Theory
Scientific paper
2006-03-09
Computer Science
Information Theory
26 pages, 7 figures, submitted to IEEE Transactions on Information Theory in Aug, 2005
Scientific paper
This paper considers the quantization problem on the Grassmann manifold \mathcal{G}_{n,p}, the set of all p-dimensional planes (through the origin) in the n-dimensional Euclidean space. The chief result is a closed-form formula for the volume of a metric ball in the Grassmann manifold when the radius is sufficiently small. This volume formula holds for Grassmann manifolds with arbitrary dimension n and p, while previous results pertained only to p=1, or a fixed p with asymptotically large n. Based on this result, several quantization bounds are derived for sphere packing and rate distortion tradeoff. We establish asymptotically equivalent lower and upper bounds for the rate distortion tradeoff. Since the upper bound is derived by constructing random codes, this result implies that the random codes are asymptotically optimal. The above results are also extended to the more general case, in which \mathcal{G}_{n,q} is quantized through a code in \mathcal{G}_{n,p}, where p and q are not necessarily the same. Finally, we discuss some applications of the derived results to multi-antenna communication systems.
Dai Wei
Liu Youjian
Rider Brian
No associations
LandOfFree
Quantization Bounds on Grassmann Manifolds and Applications to MIMO Communications does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Quantization Bounds on Grassmann Manifolds and Applications to MIMO Communications, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantization Bounds on Grassmann Manifolds and Applications to MIMO Communications will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-711555